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#ifndef lint |
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static const char RCSid[] = "$Id: bsdfrbf.c,v 2.33 2019/05/08 16:38:19 greg Exp $"; |
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#endif |
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/* |
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* Radial basis function representation for BSDF data. |
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* |
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* G. Ward |
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*/ |
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|
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/**************************************************************** |
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1) Collect samples into a grid using the Shirley-Chiu |
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angular mapping from a hemisphere to a square. |
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|
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2) Compute an adaptive quadtree by subdividing the grid so that |
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each leaf node has at least one sample up to as many |
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samples as fit nicely on a plane to within a certain |
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MSE tolerance. |
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|
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3) Place one Gaussian lobe at each leaf node in the quadtree, |
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sizing it to have a radius equal to the leaf size and |
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a volume equal to the energy in that node. |
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*****************************************************************/ |
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|
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#define _USE_MATH_DEFINES |
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#include <stdio.h> |
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#include <stdlib.h> |
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#include <string.h> |
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#include <math.h> |
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#include "bsdfrep.h" |
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|
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#ifndef RSCA |
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#define RSCA 2.0 /* radius scaling factor (empirical) */ |
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#endif |
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#ifndef MAXSLOPE |
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#define MAXSLOPE 200.0 /* maximum slope for smooth region */ |
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#endif |
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#ifndef SMOOTH_MSE |
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#define SMOOTH_MSE 5e-5 /* acceptable mean squared error */ |
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#endif |
| 40 |
#ifndef SMOOTH_MSER |
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#define SMOOTH_MSER 0.0016 /* acceptable relative MSE */ |
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#endif |
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#define MAX_RAD (GRIDRES/8) /* maximum lobe radius */ |
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|
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#define RBFALLOCB 10 /* RBF allocation block size */ |
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|
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/* loaded grid or comparison DSFs */ |
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GRIDVAL dsf_grid[GRIDRES][GRIDRES]; |
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/* allocated chrominance sums if any */ |
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float (*spec_grid)[GRIDRES][GRIDRES]; |
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int nspec_grid = 0; |
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|
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/* Set up visible spectrum sampling */ |
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void |
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set_spectral_samples(int nspec) |
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{ |
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if (rbf_colorimetry == RBCunknown) { |
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if (nspec_grid > 0) { |
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free(spec_grid); |
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spec_grid = NULL; |
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nspec_grid = 0; |
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} |
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if (nspec == 1) { |
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rbf_colorimetry = RBCphotopic; |
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return; |
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} |
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if (nspec == 3) { |
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rbf_colorimetry = RBCtristimulus; |
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spec_grid = (float (*)[GRIDRES][GRIDRES])calloc( |
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2*GRIDRES*GRIDRES, sizeof(float) ); |
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if (spec_grid == NULL) |
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goto mem_error; |
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nspec_grid = 2; |
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return; |
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} |
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fprintf(stderr, |
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"%s: only 1 or 3 spectral samples currently supported\n", |
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progname); |
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exit(1); |
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} |
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if (nspec != nspec_grid+1) { |
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fprintf(stderr, |
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"%s: number of spectral samples cannot be changed\n", |
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progname); |
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exit(1); |
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} |
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return; |
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mem_error: |
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fprintf(stderr, "%s: out of memory in set_spectral_samples()\n", |
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progname); |
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exit(1); |
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} |
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|
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/* Start new DSF input grid */ |
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void |
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new_bsdf_data(double new_theta, double new_phi) |
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{ |
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if (!new_input_direction(new_theta, new_phi)) |
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exit(1); |
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memset(dsf_grid, 0, sizeof(dsf_grid)); |
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if (nspec_grid > 0) |
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memset(spec_grid, 0, sizeof(float)*GRIDRES*GRIDRES*nspec_grid); |
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} |
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|
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/* Add BSDF data point */ |
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void |
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add_bsdf_data(double theta_out, double phi_out, const double val[], int isDSF) |
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{ |
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FVECT ovec; |
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double cfact, Yval; |
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int pos[2]; |
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|
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if (nspec_grid > 2) { |
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fprintf(stderr, "%s: unsupported color space\n", progname); |
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exit(1); |
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} |
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if (!output_orient) /* check output orientation */ |
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output_orient = 1 - 2*(theta_out > 90.); |
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else if (output_orient > 0 ^ theta_out < 90.) { |
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fprintf(stderr, |
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"%s: cannot handle output angles on both sides of surface\n", |
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progname); |
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exit(1); |
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} |
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ovec[2] = sin((M_PI/180.)*theta_out); |
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ovec[0] = cos((M_PI/180.)*phi_out) * ovec[2]; |
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ovec[1] = sin((M_PI/180.)*phi_out) * ovec[2]; |
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ovec[2] = sqrt(1. - ovec[2]*ovec[2]); |
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/* BSDF to DSF correction */ |
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cfact = isDSF ? 1. : ovec[2]; |
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|
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Yval = cfact * val[rbf_colorimetry==RBCtristimulus]; |
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/* update BSDF histogram */ |
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if (BSDF2SML*ovec[2] < Yval && Yval < BSDF2BIG*ovec[2]) |
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++bsdf_hist[histndx(Yval/ovec[2])]; |
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|
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pos_from_vec(pos, ovec); |
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|
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dsf_grid[pos[0]][pos[1]].sum.v += Yval; |
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dsf_grid[pos[0]][pos[1]].sum.n++; |
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/* add in X and Z values */ |
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if (rbf_colorimetry == RBCtristimulus) { |
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spec_grid[0][pos[0]][pos[1]] += cfact * val[0]; |
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spec_grid[1][pos[0]][pos[1]] += cfact * val[2]; |
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} |
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} |
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|
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/* Compute minimum BSDF from histogram (does not clear) */ |
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static void |
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comp_bsdf_min() |
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{ |
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unsigned long cnt, target; |
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int i; |
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|
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cnt = 0; |
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for (i = HISTLEN; i--; ) |
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cnt += bsdf_hist[i]; |
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if (!cnt) { /* shouldn't happen */ |
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bsdf_min = 0; |
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return; |
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} |
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target = cnt/100; /* ignore bottom 1% */ |
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cnt = 0; |
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for (i = 0; cnt <= target; i++) |
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cnt += bsdf_hist[i]; |
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bsdf_min = histval(i-1); |
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} |
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|
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/* Determine if the given region is empty of grid samples */ |
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static int |
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empty_region(int x0, int x1, int y0, int y1) |
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{ |
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int x, y; |
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|
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if (dsf_grid[x][y].sum.n) |
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return(0); |
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return(1); |
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} |
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|
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/* Determine if the given region is smooth enough to be a single lobe */ |
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static int |
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smooth_region(int x0, int x1, int y0, int y1) |
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{ |
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RREAL rMtx[3][3]; |
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FVECT xvec; |
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double A, B, C, nvs, sqerr; |
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int x, y, n; |
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/* compute planar regression */ |
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memset(rMtx, 0, sizeof(rMtx)); |
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memset(xvec, 0, sizeof(xvec)); |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if ((n = dsf_grid[x][y].sum.n) > 0) { |
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double z = dsf_grid[x][y].sum.v; |
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rMtx[0][0] += x*x*(double)n; |
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rMtx[0][1] += x*y*(double)n; |
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rMtx[0][2] += x*(double)n; |
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rMtx[1][1] += y*y*(double)n; |
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rMtx[1][2] += y*(double)n; |
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rMtx[2][2] += (double)n; |
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xvec[0] += x*z; |
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xvec[1] += y*z; |
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xvec[2] += z; |
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} |
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rMtx[1][0] = rMtx[0][1]; |
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rMtx[2][0] = rMtx[0][2]; |
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rMtx[2][1] = rMtx[1][2]; |
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nvs = rMtx[2][2]; |
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if (SDinvXform(rMtx, rMtx) != SDEnone) |
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return(1); /* colinear values */ |
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A = DOT(rMtx[0], xvec); |
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B = DOT(rMtx[1], xvec); |
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if (A*A + B*B > MAXSLOPE*MAXSLOPE) /* too steep? */ |
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return(0); |
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C = DOT(rMtx[2], xvec); |
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sqerr = 0.0; /* compute mean squared error */ |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if ((n = dsf_grid[x][y].sum.n) > 0) { |
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double d = A*x + B*y + C - dsf_grid[x][y].sum.v/n; |
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sqerr += n*d*d; |
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} |
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if (sqerr <= nvs*SMOOTH_MSE) /* below absolute MSE threshold? */ |
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return(1); |
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/* OR below relative MSE threshold? */ |
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return(sqerr*nvs <= xvec[2]*xvec[2]*SMOOTH_MSER); |
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} |
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|
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/* Create new lobe based on integrated samples in region */ |
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static int |
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create_lobe(RBFVAL *rvp, int x0, int x1, int y0, int y1) |
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{ |
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double vtot = 0.0; |
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double CIEXtot = 0.0, CIEZtot = 0.0; |
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int nv = 0; |
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double wxsum = 0.0, wysum = 0.0, wtsum = 0.0; |
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double rad; |
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int x, y; |
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/* compute average for region */ |
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for (x = x0; x < x1; x++) |
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for (y = y0; y < y1; y++) |
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if (dsf_grid[x][y].sum.n) { |
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const double v = dsf_grid[x][y].sum.v; |
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const int n = dsf_grid[x][y].sum.n; |
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|
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if (v > 0) { |
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const double wt = v / (double)n; |
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wxsum += wt * x; |
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wysum += wt * y; |
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wtsum += wt; |
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} |
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vtot += v; |
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nv += n; |
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if (rbf_colorimetry == RBCtristimulus) { |
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CIEXtot += spec_grid[0][x][y]; |
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CIEZtot += spec_grid[1][x][y]; |
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} |
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} |
| 261 |
if (!nv) { |
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fprintf(stderr, "%s: internal - missing samples in create_lobe\n", |
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progname); |
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exit(1); |
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} |
| 266 |
if (vtot <= 0) /* only create positive lobes */ |
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return(0); |
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/* assign color */ |
| 269 |
if (rbf_colorimetry == RBCtristimulus) { |
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const double df = 1.0 / (CIEXtot + vtot + CIEZtot); |
| 271 |
C_COLOR cclr; |
| 272 |
c_cset(&cclr, CIEXtot*df, vtot*df); |
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rvp->chroma = c_encodeChroma(&cclr); |
| 274 |
} else |
| 275 |
rvp->chroma = c_dfchroma; |
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/* peak value based on integral */ |
| 277 |
vtot *= (x1-x0)*(y1-y0)*(2.*M_PI/GRIDRES/GRIDRES)/(double)nv; |
| 278 |
rad = (RSCA/(double)GRIDRES)*(x1-x0); |
| 279 |
rvp->peak = vtot / ((2.*M_PI) * rad*rad); |
| 280 |
rvp->crad = ANG2R(rad); /* put peak at centroid */ |
| 281 |
rvp->gx = (int)(wxsum/wtsum + .5); |
| 282 |
rvp->gy = (int)(wysum/wtsum + .5); |
| 283 |
return(1); |
| 284 |
} |
| 285 |
|
| 286 |
/* Recursive function to build radial basis function representation */ |
| 287 |
static int |
| 288 |
build_rbfrep(RBFVAL **arp, int *np, int x0, int x1, int y0, int y1) |
| 289 |
{ |
| 290 |
int xmid = (x0+x1)>>1; |
| 291 |
int ymid = (y0+y1)>>1; |
| 292 |
int branched[4]; |
| 293 |
int nadded, nleaves; |
| 294 |
/* need to make this a leaf? */ |
| 295 |
if (empty_region(x0, xmid, y0, ymid) || |
| 296 |
empty_region(xmid, x1, y0, ymid) || |
| 297 |
empty_region(x0, xmid, ymid, y1) || |
| 298 |
empty_region(xmid, x1, ymid, y1)) |
| 299 |
return(0); |
| 300 |
/* add children (branches+leaves) */ |
| 301 |
if ((branched[0] = build_rbfrep(arp, np, x0, xmid, y0, ymid)) < 0) |
| 302 |
return(-1); |
| 303 |
if ((branched[1] = build_rbfrep(arp, np, xmid, x1, y0, ymid)) < 0) |
| 304 |
return(-1); |
| 305 |
if ((branched[2] = build_rbfrep(arp, np, x0, xmid, ymid, y1)) < 0) |
| 306 |
return(-1); |
| 307 |
if ((branched[3] = build_rbfrep(arp, np, xmid, x1, ymid, y1)) < 0) |
| 308 |
return(-1); |
| 309 |
nadded = branched[0] + branched[1] + branched[2] + branched[3]; |
| 310 |
nleaves = !branched[0] + !branched[1] + !branched[2] + !branched[3]; |
| 311 |
if (!nleaves) /* nothing but branches? */ |
| 312 |
return(nadded); |
| 313 |
/* combine 4 leaves into 1? */ |
| 314 |
if ((nleaves == 4) & (x1-x0 <= MAX_RAD) && |
| 315 |
smooth_region(x0, x1, y0, y1)) |
| 316 |
return(0); |
| 317 |
/* need more array space? */ |
| 318 |
if ((*np+nleaves-1)>>RBFALLOCB != (*np-1)>>RBFALLOCB) { |
| 319 |
*arp = (RBFVAL *)realloc(*arp, |
| 320 |
sizeof(RBFVAL)*(*np+nleaves-1+(1<<RBFALLOCB))); |
| 321 |
if (*arp == NULL) |
| 322 |
return(-1); |
| 323 |
} |
| 324 |
/* create lobes for leaves */ |
| 325 |
if (!branched[0] && create_lobe(*arp+*np, x0, xmid, y0, ymid)) { |
| 326 |
++(*np); ++nadded; |
| 327 |
} |
| 328 |
if (!branched[1] && create_lobe(*arp+*np, xmid, x1, y0, ymid)) { |
| 329 |
++(*np); ++nadded; |
| 330 |
} |
| 331 |
if (!branched[2] && create_lobe(*arp+*np, x0, xmid, ymid, y1)) { |
| 332 |
++(*np); ++nadded; |
| 333 |
} |
| 334 |
if (!branched[3] && create_lobe(*arp+*np, xmid, x1, ymid, y1)) { |
| 335 |
++(*np); ++nadded; |
| 336 |
} |
| 337 |
return(nadded); |
| 338 |
} |
| 339 |
|
| 340 |
/* Count up filled nodes and build RBF representation from current grid */ |
| 341 |
RBFNODE * |
| 342 |
make_rbfrep() |
| 343 |
{ |
| 344 |
RBFNODE *newnode; |
| 345 |
RBFVAL *rbfarr; |
| 346 |
int nn; |
| 347 |
/* compute minimum BSDF */ |
| 348 |
comp_bsdf_min(); |
| 349 |
/* create RBF node list */ |
| 350 |
rbfarr = NULL; nn = 0; |
| 351 |
if (build_rbfrep(&rbfarr, &nn, 0, GRIDRES, 0, GRIDRES) <= 0) { |
| 352 |
if (nn) |
| 353 |
goto memerr; |
| 354 |
fprintf(stderr, |
| 355 |
"%s: warning - skipping bad incidence (%.1f,%.1f)\n", |
| 356 |
progname, theta_in_deg, phi_in_deg); |
| 357 |
return(NULL); |
| 358 |
} |
| 359 |
/* (re)allocate RBF array */ |
| 360 |
newnode = (RBFNODE *)realloc(rbfarr, |
| 361 |
sizeof(RBFNODE) + sizeof(RBFVAL)*(nn-1)); |
| 362 |
if (newnode == NULL) |
| 363 |
goto memerr; |
| 364 |
/* copy computed lobes into RBF node */ |
| 365 |
memmove(newnode->rbfa, newnode, sizeof(RBFVAL)*nn); |
| 366 |
newnode->ord = -1; |
| 367 |
newnode->next = NULL; |
| 368 |
newnode->ejl = NULL; |
| 369 |
newnode->invec[2] = sin((M_PI/180.)*theta_in_deg); |
| 370 |
newnode->invec[0] = cos((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
| 371 |
newnode->invec[1] = sin((M_PI/180.)*phi_in_deg)*newnode->invec[2]; |
| 372 |
newnode->invec[2] = input_orient*sqrt(1. - newnode->invec[2]*newnode->invec[2]); |
| 373 |
newnode->vtotal = .0; |
| 374 |
newnode->nrbf = nn; |
| 375 |
/* compute sum for normalization */ |
| 376 |
while (nn-- > 0) |
| 377 |
newnode->vtotal += rbf_volume(&newnode->rbfa[nn]); |
| 378 |
#ifdef DEBUG |
| 379 |
fprintf(stderr, "Built RBF with %d lobes\n", newnode->nrbf); |
| 380 |
fprintf(stderr, "Integrated DSF at (%.1f,%.1f) deg. is %.2f\n", |
| 381 |
get_theta180(newnode->invec), get_phi360(newnode->invec), |
| 382 |
newnode->vtotal); |
| 383 |
#endif |
| 384 |
if (insert_dsf(newnode) < 0) |
| 385 |
return(NULL); |
| 386 |
return(newnode); |
| 387 |
memerr: |
| 388 |
fprintf(stderr, "%s: Out of memory in make_rbfrep()\n", progname); |
| 389 |
exit(1); |
| 390 |
} |
